Pixel to Gaussian: Ultra-Fast Continuous Super-Resolution with 2D Gaussian Modeling

Arbitrary-scale super-resolution (ASSR) aims to reconstruct high-resolution (HR) images from low-resolution (LR) inputs with arbitrary upsampling factors using a single model, addressing the limitations of traditional SR methods constrained to fixed-scale factors (\textit{e.g.}, $\times$ 2). Recent advances leveraging implicit neural representation (INR) have achieved great progress by modeling coordinate-to-pixel mappings. However, the efficiency of these methods may suffer from repeated upsampling and decoding, while their reconstruction fidelity and quality are constrained by the intrinsic representational limitations of coordinate-based functions. To address these challenges, we propose a novel ContinuousSR framework with a Pixel-to-Gaussian paradigm, which explicitly reconstructs 2D continuous HR signals from LR images using Gaussian Splatting. This approach eliminates the need for time-consuming upsampling and decoding, enabling extremely fast ASSR. Once the Gaussian field is built in a single pass, ContinuousSR can perform arbitrary-scale rendering in just 1ms per scale. Our method introduces several key innovations. Through statistical analysis, we uncover the Deep Gaussian Prior (DGP) and propose DGP-Driven Covariance Weighting, which dynamically optimizes covariance via adaptive weighting. Additionally, we present Adaptive Position Drifting, which refines the positional distribution of the Gaussian space based on image content, further enhancing reconstruction quality. Extensive experiments on seven benchmarks demonstrate that our ContinuousSR delivers significant improvements in SR quality across all scales, with an impressive 19.5× speedup when continuously upsampling an image across forty scales.